Bayesian estimation of dynamic mixture models by wavelets using horseshoe prior

• Grant number: 26/12377-1
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: September 01, 2026
• End date: August 31, 2027
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Statistics
• Principal Investigator: Michel Helcias Montoril
• Grantee: Gabriela Lins de Albuquerque
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil

Abstract

Modeling heterogeneous data through mixture models has attracted increasing interest in Statistics, especially when mixture weights exhibit dynamic behavior over time or space. Recently, Motta and Montoril (2026) proposed a Bayesian approach for estimating dynamic mixture models using wavelets, where the wavelet coefficients are estimated via Gaussian and Laplace spike-and-slab priors. In this undergraduate research project, we propose to study and implement an alternative to these priors: the horseshoe prior. The horseshoe prior is a continuous shrinkage prior with appealing theoretical and empirical properties for sparse signal estimation, mimicking the behavior of the spike-and-slab prior without requiring the specification of a discrete mixture. We expect that incorporating the horseshoe prior into the existing Gibbs sampling algorithm will improve the estimation of dynamic mixture weights, particularly in scenarios involving irregular weight functions. The activities will be carried out over twelve months, including computational implementation in R, Monte Carlo simulation studies, and real-world data applications. (AU)